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Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints. A. Häusler 1 , R. Ghabcheloo 2 , A. Pascoal 1 , A. Aguiar 1 1 Instituto Superior Técnico, Lisbon, Portugal 2 Tampere University of Technology, Tampere, Finland. Introduction.

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multiple marine vehile deconflicted path planning with currents and communication constraints

Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints

A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1

1Instituto Superior Técnico, Lisbon, Portugal

2Tampere University of Technology, Tampere, Finland

introduction
Introduction
  • Efficient algorithms for multiple vehicle path planning are crucial for cooperative control systems
  • Need to take into account vehicle dynamics, mission parameters and external influences
  • Example: Go-To-Formation maneouvre

Andreas J. Häusler - IAV 2010

the go to formation maneouvre
The Go-To-Formation Maneouvre

Current

Mother Ship

  • An initial formation pattern must be established before mission start
  • Deploying the vehicles cannot be done in formation (no hovering capabilities)
  • Vehicles can’t be driven to target positions separately (no hovering capabilities)

Andreas J. Häusler - IAV 2010

the go to formation maneouvre1
The Go-To-Formation Maneouvre

Mother Ship

  • Need to drive the vehicles to the initial formation in a concerted manner
  • Ensure simultaneous arrival times and equal speeds
  • Establish collision avoidance through maintaining a spatial clearance

Andreas J. Häusler - IAV 2010

path planning foundations
Path Planning Foundations

Final position

Initial position

Andreas J. Häusler - IAV 2010

polynomial path planning
Polynomial Path Planning
  • Dispense with absolute time in planning a path (Yakimenko)
  • Establish timing laws describing the evolution of nominal speed with
  • Spatial and temporal constraints are thereby decoupled and captured by &
  • Choose and as polynomials
  • Path shape changes with only varying

Andreas J. Häusler - IAV 2010

polynomial path planning1
Polynomial Path Planning
  • Polynomial for each coordinate with degree determined by the number of boundary conditions
  • Temporal speed and acceleration constraints
  • Choice for timing law with

Andreas J. Häusler - IAV 2010

cost function considerations
CostFunctionConsiderations

Andreas J. Häusler - IAV 2010

cost function considerations1
Cost Function Considerations
  • A path is feasible if it can be tracked by a vehicle without exceeding , , and
  • It can be obtained by minimizing the energy consumption
  • subject to temporal speed and acceleration constraints

Andreas J. Häusler - IAV 2010

multiple vehicle path planning
Multiple Vehicle Path Planning
  • Instead of trying to minimize the arrival time interval, we can fix arrival times to be exactly equal and still get different path shapes
  • Integrate for

Andreas J. Häusler - IAV 2010

multiple vehicle path planning1
Multiple Vehicle Path Planning
  • Then we obtain , from which the spatial paths are computed
  • The result is in turn used to compute velocity and acceleration
  • Optimization is done using direct search

Andreas J. Häusler - IAV 2010

spatial deconfliction
Spatial Deconfliction

Final positions

(target formation)

Initial positions

Andreas J. Häusler - IAV 2010

temporal deconfliction
Temporal Deconfliction

Final positions

(target formation)

Initial positions

Andreas J. Häusler - IAV 2010

deconfliction
Deconfliction
  • Spatial deconfliction: subject to
  • For temporal deconfliction, the constraint changes to
  • Simultaneous arrival at time

Andreas J. Häusler - IAV 2010

environmental constraints
Environmental Constraints
  • Incorporated throughbarrier function
  • Path planningwithcurrentsformoreenergy-efficientpaths (insteadofsolelyrelying on pathfollowingcontroller)
  • Path planningwithcommunicationconstraintsforrangekeepingwithinthegroup

(Hauser, CDC 2006)

Andreas J. Häusler - IAV 2010

path planning system
Path Planning System

MissionSpecifications

SpatialClearance

Optimization Algorithm

Comm. Constraint

CostCriterion

PathGeneration

InitialGuess

AMV

Data

Init. Position & Heading

Path

Nominal Paths

InitialVelocity

Time-CoordinatedPathFollowing

Final Position & Heading

Revised Guess

SpeedProfiles

Final Velocity

DynamicalConstraints

EnvironmentalConstraints

Current

Obstacles

Andreas J. Häusler - IAV 2010

time coordinated path following
Time-Coordinated Path Following
  • Closed-form solution to problems of open-loop path planning and trajectory tracking
  • Using virtual time with

(Ghabcheloo, ACC 2009)

Andreas J. Häusler - IAV 2010

time coordinated path following1
Time-Coordinated Path Following
  • Path followingcontrolstrategy
  • Guaranteesthatvehiclesandaredeconflictedandthattheyfollowtheirtrajectoryif
  • A time coordinationcontrollawcanbefound so thatthemissionremains “near optimal“ in thepresenceofdisturbances

Andreas J. Häusler - IAV 2010

simulation results
Simulation Results
  • Algorithm makes use of currents to minimize expected energy usage
  • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax

Andreas J. Häusler - IAV 2010

simulation results1
Simulation Results
  • Algorithm makes use of currents to minimize expected energy usage
  • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax

Andreas J. Häusler - IAV 2010

simulation results2
Simulation Results
  • Communication constraints with and without spatial deconfliction
  • Communication break distance 50m and 80m

Andreas J. Häusler - IAV 2010

conclusions
Conclusions
  • Recent improvements of the planner include currents and communication constraints
  • Thereby enhances usability for mission planning
  • Barrier function approach allows for “probing” the path limits (useful for obstacle avoidance)
  • Algorithm easily adaptable for arbitrary number of vehicles

Andreas J. Häusler - IAV 2010

future work
Future Work
  • Running time increases exponentially with number of discrete points  use different optimization approach and/or different means of path description
  • Incorporate real vehicle dynamics instead of approximation through constraints
  • Improve communication constraint
  • Use more sophisticated energy usage equation
  • Allow for specification of vehicle sub-groups

Andreas J. Häusler - IAV 2010

thank you for your attention
Thank you for your attention!

Outlook: trajectoryoptimizationusing a projectionoperatorapproach

(blue: desiredpath, green: timeandenergyoptimalpathaccording to vehicledynamics

Outlook: obstacleavoidanceusing the projectionoperator

Outlook: collisionavoidanceusing the projectionoperator

Outlook: obstacle and collision avoidance

using a projection operatoroptimization

approach

Andreas J. Häusler - IAV 2010